Problem: Simplify the following expression: $p = \dfrac{-45q - 35}{-45q - 45}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-45q - 35 = - (3\cdot3\cdot5 \cdot q) - (5\cdot7)$ The denominator can be factored: $-45q - 45 = - (3\cdot3\cdot5 \cdot q) - (3\cdot3\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $p = \dfrac{(5)(-9q - 7)}{(5)(-9q - 9)}$ Dividing both the numerator and denominator by $5$ gives: $p = \dfrac{-9q - 7}{-9q - 9}$